TY - JOUR
T1 - Bistable plates for morphing structures
T2 - A refined analytical approach with high-order polynomials
AU - Pirrera, A.
AU - Avitabile, D.
AU - Weaver, P. M.
PY - 2010/12/15
Y1 - 2010/12/15
N2 - The multistability of composite thin structures has shown potential for morphing applications. The present work combines a Ritz model with path-following algorithms to study bistable plates' behaviour. Classic low-order Ritz models predict stable shapes' geometry with reasonable accuracy. However, they may fail when modelling other aspects of the elastic structural behaviour. A refined higher-order model is here presented. In order to improve the inherently poor conditioning properties of Ritz approximations of slender structures, a non-dimensional version of Classical Plate Lamination Theory with von Kármán nonlinear strains is developed and presented. In the current approach, we continue numerical solutions in parameter space, that is, we path-follow equilibrium configurations as the control parameter varies, find stable and unstable configurations and identify bifurcations. The numerics are carried out using a set of in-house Matlab® routines for numerical continuation. The increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour. Finally, the complex, experimentally observed snap-through geometry is captured analytically for the first time. Results are validated against finite elements analysis throughout the course of the paper.
AB - The multistability of composite thin structures has shown potential for morphing applications. The present work combines a Ritz model with path-following algorithms to study bistable plates' behaviour. Classic low-order Ritz models predict stable shapes' geometry with reasonable accuracy. However, they may fail when modelling other aspects of the elastic structural behaviour. A refined higher-order model is here presented. In order to improve the inherently poor conditioning properties of Ritz approximations of slender structures, a non-dimensional version of Classical Plate Lamination Theory with von Kármán nonlinear strains is developed and presented. In the current approach, we continue numerical solutions in parameter space, that is, we path-follow equilibrium configurations as the control parameter varies, find stable and unstable configurations and identify bifurcations. The numerics are carried out using a set of in-house Matlab® routines for numerical continuation. The increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour. Finally, the complex, experimentally observed snap-through geometry is captured analytically for the first time. Results are validated against finite elements analysis throughout the course of the paper.
KW - Adimensional model
KW - Bistability
KW - Composite plates
KW - Conditioning number
KW - Nonlinear
KW - Numerical continuation
KW - Parametric analysis
KW - Ritz method
UR - http://www.scopus.com/inward/record.url?scp=77958021913&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77958021913&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2010.08.019
DO - 10.1016/j.ijsolstr.2010.08.019
M3 - Article
AN - SCOPUS:77958021913
SN - 0020-7683
VL - 47
SP - 3412
EP - 3425
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 25-26
ER -